We investigate the dynamics of pore-driven polymer translocation by theoretical analysis and molecular dynamics (MD) simulations. Using the tension propagation theory within the constant flux approximation we derive an explicit equation of motion for the tension front. From this we derive a scaling relation for the average translocation time τ, which captures the asymptotic result

$\tau \propto N_0^{1+\nu }$
τN01+ν⁠, where N0 is the chain length and ν is the Flory exponent. In addition, we derive the leading correction-to-scaling term to τ and show that all terms of order
$N_0^{2\nu }$
N02ν
exactly cancel out, leaving only a finite-chain length correction term due to the effective pore friction, which is linearly proportional to N0. We use the model to numerically include fluctuations in the initial configuration of the polymer chain in addition to thermal noise. We show that when the cis side fluctuations are properly accounted for, the model not only reproduces previously known results but also considerably improves the estimates of the monomer waiting time distribution and the time evolution of the translocation coordinate s(t), showing excellent agreement with MD simulations.

1.
J. J.
Kasianowicz
,
E.
Brandin
,
D.
Branton
, and
D. W.
Deamer
,
Proc. Natl. Acad. Sci. U. S. A.
93
,
13770
(
1996
).
2.
A.
Meller
,
J. Phys. Condens. Matter
15
,
R581
(
2003
).
3.
M.
Muthukumar
,
Polymer Translocation
(
Taylor & Francis
,
2011
).
4.
A.
Milchev
,
J. Phys.: Condens. Matter
23
,
103101
(
2011
).
5.
V. V.
Palyulin
,
T.
Ala-Nissila
, and
R.
Metzler
,
Soft Matter
10
,
9016
(
2014
).
6.
E. E.
Schadt
,
S.
Turner
, and
A.
Kasarskis
,
Hum. Mol. Genet.
19
,
R227
(
2010
).
7.
D.
Branton
and
D. W.
Deamer
,
A.
Marziali
 et al
Nat. Biotechnol.
26
,
1146
(
2008
).
8.
A. J.
Storm
 et al,
Nano Lett.
5
,
1193
(
2005
).
9.
W.
Sung
and
P. J.
Park
,
Phys. Rev. Lett.
77
,
783
(
1996
).
10.
M.
Muthukumar
,
J. Chem. Phys.
111
,
10371
(
1999
).
11.
J.
Chuang
,
Y.
Kantor
, and
M.
Kardar
,
Phys. Rev. E
65
,
011802
(
2001
).
12.
R.
Metzler
and
J.
Klafter
,
Biophys. J.
85
,
2776
(
2003
).
13.
Y.
Kantor
and
M.
Kardar
,
Phys. Rev. E
69
,
021806
(
2004
).
14.
K.
Luo
,
S. T. T.
Ollila
,
I.
Huopaniemi
,
T.
Ala-Nissila
,
P.
Pomorski
,
M.
Karttunen
,
S.-C.
Ying
, and
A.
Bhattacharya
,
Phys. Rev. E
78
,
050901
(R) (
2008
).
15.
K.
Luo
,
T.
Ala-Nissila
,
S.-C.
Ying
, and
R.
Metzler
,
Europhys. Lett.
88
,
68006
(
2009
).
16.
J. L. A.
Dubbeldam
,
A.
Milchev
,
V. G.
Rostiashvili
, and
T. A.
Vilgis
,
Europhys. Lett.
79
,
18002
(
2007
).
17.
A. Yu.
Grosberg
,
S.
Nechaev
,
M.
Tamm
, and
O.
Vasilyev
,
Phys. Rev. Lett.
96
,
228105
(
2006
).
18.
19.
T.
Sakaue
,
AIP Conf. Proc.
982
,
508
(
2008
).
20.
21.
T.
Saito
and
T.
Sakaue
,
Eur. Phys. J. E
34
,
135
(
2012
).
22.
T.
Saito
and
T.
Sakaue
,
Phys. Rev. E
85
,
061803
(
2012
).
23.
T.
Saito
and
T.
Sakaue
, “
Two phase picture in driven polymer translocation
,” preprint arXiv:1205.3861 (
2012
).
24.
P.
Rowghanian
and
A. Y.
Grosberg
,
J. Phys. Chem. B
115
,
14127
(
2011
).
25.
J. L. A.
Dubbeldam
,
V. G.
Rostiashvili
,
A.
Milchev
, and
T. A.
Vilgis
,
Phys. Rev. E
85
,
041801
(
2012
).
26.
T.
Ikonen
,
A.
Bhattacharya
,
T.
Ala-Nissila
, and
W.
Sung
,
Phys. Rev. E
85
,
051803
(
2012
).
27.
T.
Ikonen
,
A.
Bhattacharya
,
T.
Ala-Nissila
, and
W.
Sung
,
J. Chem. Phys.
137
,
085101
(
2012
).
28.
T.
Ikonen
,
A.
Bhattacharya
,
T.
Ala-Nissila
, and
W.
Sung
,
Europhys. Lett
103
,
38001
(
2013
).
29.
V.
Lehtola
,
R. P.
Linna
, and
K.
Kaski
,
Europhys. Lett.
85
,
58006
(
2009
).
30.
A.
Bhattacharya
,
W. H.
Morrison
,
K.
Luo
,
T.
Ala-Nissila
,
S.-C.
Ying
,
A.
Milchev
, and
K.
Binder
,
Eur. Phys. J. E
29
,
423
(
2009
).
31.
V. V.
Lehtola
,
K.
Kaski
, and
R. P.
Linna
,
Phys. Rev. E
82
,
031908
(
2010
).
32.
A.
Bhattacharya
and
K.
Binder
,
Phys. Rev. E
81
,
041804
(
2010
).
33.
H. W.
de Haan
and
G. W.
Slater
,
Phys. Rev. E
81
,
051802
(
2010
).
34.
H. W.
de Haan
and
G. W.
Slater
,
J. Chem. Phys.
136
,
204902
(
2012
).
35.
M. G.
Gauthier
and
G. W.
Slater
,
Phys. Rev. E
79
,
021802
(
2009
).
36.
J. M.
Polson
and
A. C. M.
McCaffrey
,
J. Chem. Phys.
138
,
174902
(
2013
).
37.
P. M.
Suhonen
,
K.
Kaski
, and
R.
Linna
,
Phys. Rev. E
90
,
042702
(
2014
).
38.
J. L. A.
Dubbeldam
,
V. G.
Rostiashvili
, and
T. A.
Vilgis
,
J. Chem. Phys.
141
,
124112
(
2014
).
39.
E. A.
DiMarzio
,
C. M.
Guttman
, and
J. D.
Hoffman
,
Faraday Discuss. Chem. Soc.
68
,
210
(
1979
).
40.
A. F.
Sauer-Budge
,
J. A.
Nyamwanda
,
D. K.
Lubensky
, and
D.
Branton
,
Phys. Rev. Lett.
90
,
238101
(
2003
).
41.
J.
Mathe
,
H.
Visram
,
V.
Viasnoff
,
Y.
Rabin
, and
A.
Meller
,
Biophys. J.
87
,
3205
(
2004
).
42.
T.
Ikonen
,
J.
Shin
,
W.
Sung
, and
T.
Ala-Nissila
,
J. Chem. Phys.
136
,
205104
(
2012
).
43.
J. L. A.
Dubbeldam
,
V. G.
Rostiashvili
,
A.
Milchev
, and
T. A.
Vilgis
,
Phys. Rev. E
87
,
032147
(
2013
).
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